The paper develops a simple economic model of a biological invasion. The natural growth of t he invasion is non-convex and the immediate cost of controlling the invasion depends on the level of current control as well as the current size of the invasion. Greater control raises contr ol costs today while reducing damages - now and in the future. In addition, by decreasing the size of the invasion, inc reased control today raises the marginal cost of control in the future. As a consequence, the optim al path of an invasion is not necessarily monotonic. When the marginal control cost declines sharply with the size of invasion, it may be optimal to allow an invasion to grow naturally before it is controll ed. We characterize conditions under which it is optimal to eradicate an invasive speci es (immediately and eventually) and conditions under which it is optimal to manage an invasion without complete eradication.